Average Error: 0.2 → 0.2
Time: 17.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(m + \frac{m}{\frac{v}{m \cdot m}}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(m + \frac{m}{\frac{v}{m \cdot m}}\right)
double f(double m, double v) {
        double r984940 = m;
        double r984941 = 1.0;
        double r984942 = r984941 - r984940;
        double r984943 = r984940 * r984942;
        double r984944 = v;
        double r984945 = r984943 / r984944;
        double r984946 = r984945 - r984941;
        double r984947 = r984946 * r984940;
        return r984947;
}
↓
double f(double m, double v) {
        double r984948 = m;
        double r984949 = v;
        double r984950 = r984949 / r984948;
        double r984951 = r984948 / r984950;
        double r984952 = r984948 * r984948;
        double r984953 = r984949 / r984952;
        double r984954 = r984948 / r984953;
        double r984955 = r984948 + r984954;
        double r984956 = r984951 - r984955;
        return r984956;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.6

    \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \color{blue}{\left(\sqrt{m} \cdot \sqrt{m}\right)}\]

  4. Applied associate-*r*0.6

    \[\leadsto \color{blue}{\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \sqrt{m}\right) \cdot \sqrt{m}}\]

  5. Taylor expanded around 0 7.2

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  6. Simplified0.2

    \[\leadsto \color{blue}{\frac{m}{\frac{v}{m}} - \left(m + \frac{m}{\frac{v}{m \cdot m}}\right)}\]

  7. Final simplification0.2

    \[\leadsto \frac{m}{\frac{v}{m}} - \left(m + \frac{m}{\frac{v}{m \cdot m}}\right)\]

Reproduce

herbie shell --seed 2019164 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))